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Baltic Way
2015 Baltic Way
15
15
Part of
2015 Baltic Way
Problems
(1)
Geometry
Source: Baltic Way 2015
11/8/2015
In triangle
A
B
C
ABC
A
BC
, the interior and exterior angle bisectors of
∠
B
A
C
\angle BAC
∠
B
A
C
intersect the line
B
C
BC
BC
in
D
D
D
and
E
E
E
, respectively. Let
F
F
F
be the second point of intersection of the line
A
D
AD
A
D
with the circumcircle of the triangle
A
B
C
ABC
A
BC
. Let
O
O
O
be the circumcentre of the triangle
A
B
C
ABC
A
BC
and let
D
′
D'
D
′
be the reflection of
D
D
D
in
O
O
O
. Prove that
∠
D
′
F
E
=
90.
\angle D'FE =90.
∠
D
′
FE
=
90.
geometry
Baltic Way